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Loan Workouts: Putting it All Together
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Loan Workouts So far we’ve looked at: Probability of success and failure over the entire loan records P(S) = 0.464 P(F) = 0.536 Expected Value of Workout E(X) = (Full Loan) P(S) + (Default) P(F)
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Loan Workouts We also looked at the conditional probabilities of success and failure based on Y, T, and C P(S|Y) P(F|Y) P(S|T) P(F|T) P(S|C) P(F|C)
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Loan Workouts We also looked at the expected value of each of our borrowers characteristics: E(Z Y ) E(Z T ) E(Z C ) Unfortunately, none of these pieces of info helps for making a decision for our particular borrower
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Loan Workouts We would like to be able find out expected value and probabilities using all of our borrower’s characteristics In other words: P(S|Y&T&C) AND P(F|Y&T&C) E(Z)
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Loan Workouts Unfortunately our loan records do NOT contain enough information to compute P(S|Y&T&C) AND P(F|Y&T&C) Why? The loan records are incomplete across the three banks that were merged Customer #1 in the loan records has information with respect to education level only No Info on Years of Business Experience or Economic Times
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Loan Workouts Bayes’ Theorem to rescue Allow us to find: If we know:
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Loan Workouts How? But the numerator portion can be expressed as:
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Loan Workouts How do we compute: One of the project assumptions is that Y, T, and C are all independent of each other event if we consider successes or failures
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Loan Workouts Knowing this we can say: We know need to find
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Loan Workouts Let’s look at one of these and figure out its probability. Computations will be similar for the other two Consider: This is asking for the probability a borrower has the same # of years experience as your borrower given the workout was successful
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Loan Workouts Because BR Bank was the only bank to keep records on borrowers years of experience, we only have their records to rely on: But since we can assume each bank made out loans to similar populations of borrowers, our estimation is a good one
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Loan Workouts To find
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Loan Workouts So if reproduce the same calculation for the other conditional probabilities we now know: From this we can also do similar calculations for:
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Loan Work Out Tree Diagram S F (Y T C) (Y T C) C (Y T C) (Y T C) C P(S)P(S) P(F)P(F) P(Y T C | S) P(Y T C | F) P(S Y T C) = P(S). P(Y T C | S) = P(S). P(Y|S). P(T|S). P(C|S) P(F Y T C) = P(F). P(Y T C | F) = P(F). P(Y|F). P(T|F). P(C|F)
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